Graphing Equation in HTML5 Using Canvas

Ashwani Tyagi
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Introduction

In this article I will walk through how to use a graphing equation in a HTML5 canvas.

Graphing Equation in HTML5 using Canvas

What is the Graph of an Equation?

It is the set of points where the equation is true.

Features of a Graph

For a graph to be "complete" you need to show all the important features.

Peaks
Valleys
Flat Areas
Asymptotes
Any other special feature

Browser Support

It is supported by all major browsers such as Internet Explorer 9, Firefox 3.6+, Safari 4+ and Chrome etc.

Procedure for creating the graphing equations

Step 1

We first define the element using a "canvas" in HTML5. The height and width attributes set the canvas and graph size.

Step 2

In order to interact with this canvas through JavaScript, we will need to first get the element by Id and then create a context.

var canvas = document.getElementById('mycanvas');

var ctx = canvas.getContext("2d");

</script>

Step 3

In the following code we will create a "Graph" function in which we define various methods, variables, constants and properties.

function Graph(config)

{

// user defined properties

this.canvas = document.getElementById(config.canvasId);

this.minX = config.minX;

this.minY = config.minY;

this.maxX = config.maxX;

this.maxY = config.maxY;

this.unitsPerTick = config.unitsPerTick;

// constants

this.axisColor = "#aaa";

this.font = "8pt Calibri";

this.tickSize = 20;

// relationships

this.context = this.canvas.getContext("2d");

this.rangeX = this.maxX - this.minX;

this.rangeY = this.maxY - this.minY;

this.unitX = this.canvas.width / this.rangeX;

this.unitY = this.canvas.height / this.rangeY;

this.centerY = Math.round(Math.abs(this.minY / this.rangeY) * this.canvas.height);

this.centerX = Math.round(Math.abs(this.minX / this.rangeX) * this.canvas.width);

this.iteration = (this.maxX - this.minX) / 1000;

this.scaleX = this.canvas.width / this.rangeX;

this.scaleY = this.canvas.height / this.rangeY;

// draw x and y axis

this.drawXAxis();

this.drawYAxis();

}

Step 4

In the following code we will draw the x-axis. On the x-axis we draw the left tick marks and then draw the right tick marks. For drawing both of the tick marks we apply the loop.

Graph.prototype.drawXAxis = function ()

{

var context = this.context;

context.save();

context.beginPath();

context.moveTo(0, this.centerY);

context.lineTo(this.canvas.width, this.centerY);

context.strokeStyle = this.axisColor;

context.lineWidth = 2;

context.stroke();

Figure 1

The following figure represents the x-axis:

// draw tick marks

var xPosIncrement = this.unitsPerTick * this.unitX;

var xPos, unit;

context.font = this.font;

context.textAlign = "center";

context.textBaseline = "top";

// draw left tick marks

xPos = this.centerX - xPosIncrement;

unit = -1 * this.unitsPerTick;

while (xPos > 0)

{

context.moveTo(xPos, this.centerY - this.tickSize / 2);

context.lineTo(xPos, this.centerY + this.tickSize / 2);

context.stroke();

context.fillText(unit, xPos, this.centerY + this.tickSize / 2 + 3);

unit -= this.unitsPerTick;

xPos = Math.round(xPos - xPosIncrement);

}

Figure 2

The following figure represents the left side tick mark of the x-axis:

// draw right tick marks

xPos = this.centerX + xPosIncrement;

unit = this.unitsPerTick;

while (xPos < this.canvas.width)

{

context.moveTo(xPos, this.centerY - this.tickSize / 2);

context.lineTo(xPos, this.centerY + this.tickSize / 2);

context.stroke();

context.fillText(unit, xPos, this.centerY + this.tickSize / 2 + 3);

unit += this.unitsPerTick;

xPos = Math.round(xPos + xPosIncrement);

}

context.restore();

};

Figure 3

The following figure represents the right side tick mark of the x-axis:

Step 5

Similarily, we will draw the y-axis. On y-axis we will draw the tick marks along the upper side of the y-axis and finally we draw the tick mark for the bottom side of the y-axis. For drawing both of the tick marks and labels we apply the loop.

Graph.prototype.drawYAxis = function ()

{

var context = this.context;

context.save();

context.beginPath();

context.moveTo(this.centerX, 0);

context.lineTo(this.centerX, this.canvas.height);

context.strokeStyle = this.axisColor;

context.lineWidth = 2;

context.stroke();

Figure 4

The following figure represents the y-axis:

// draw tick marks

var yPosIncrement = this.unitsPerTick * this.unitY;

var yPos, unit;

context.font = this.font;

context.textAlign = "right";

context.textBaseline = "middle";

// draw top tick marks

yPos = this.centerY - yPosIncrement;

unit = this.unitsPerTick;

while (yPos > 0)

{

context.moveTo(this.centerX - this.tickSize / 2, yPos);

context.lineTo(this.centerX + this.tickSize / 2, yPos);

context.stroke();

context.fillText(unit, this.centerX - this.tickSize / 2 - 3, yPos);

unit += this.unitsPerTick;

yPos = Math.round(yPos - yPosIncrement);

}

Figure 5

The following figure represents the upper side tick mark on the y-axis:

// draw bottom tick marks

yPos = this.centerY + yPosIncrement;

unit = -1 * this.unitsPerTick;

while (yPos < this.canvas.height)

{

context.moveTo(this.centerX - this.tickSize / 2, yPos);

context.lineTo(this.centerX + this.tickSize / 2, yPos);

context.stroke();

context.fillText(unit, this.centerX - this.tickSize / 2 - 3, yPos);

unit -= this.unitsPerTick;

yPos = Math.round(yPos + yPosIncrement);

}

context.restore();

};

Figure 6

The following figure represent the lower side of the y-axis:

Figure 7

The following figure represents the combination of x-axis and y-axis. Both form a graph.

Step 6

In the following step we will draw the equation on the graph. We will apply the loop for drawing the equation.

Graph.prototype.drawEquation = function (equation, color, thickness)

{

var context = this.context;

context.save();

this.transformContext();

context.beginPath();

context.moveTo(this.minX, equation(this.minX));

for (var x = this.minX + this.iteration; x <= this.maxX; x += this.iteration)

{

context.lineTo(x, equation(x));

}

context.restore();

context.lineJoin = "round";

context.lineWidth = thickness;

context.strokeStyle = color;

context.stroke();

context.restore();

};

Step 7

We will transform the context to move it to the center. Then we will stretch the grid to fit the canvas window, and invert the y scale so that it increments as you move upwards.

Graph.prototype.transformContext = function ()

{

var context = this.context;

// move context to center of canvas

this.context.translate(this.centerX, this.centerY);

context.scale(this.scaleX, -this.scaleY);

};

Step 8

In the following code the window onload we will draw lines on the graph.

window.onload = function ()

{

var myGraph = new Graph({

canvasId: "myCanvas",

minX: -10,

minY: -10,

maxX: 10,

maxY: 10,

unitsPerTick: 1

});

myGraph.drawEquation(function (x) {

return 5 * Math.sin(x);

}, "green", 3);

myGraph.drawEquation(function (x) {

return x * x;

}, "blue", 3);

myGraph.drawEquation(function (x) {

return 1 * x;

}, "red", 3);

};

Example

<!DOCTYPE html>

<head>

<title>Graphing Equation in HTML5</title>

function Graph(con) {

// user defined properties

this.canvas = document.getElementById(con.canvasId);

this.minX = con.minX;

this.minY = con.minY;

this.maxX = con.maxX;

this.maxY = con.maxY;

this.unitsPerTick = con.unitsPerTick;

// constants

this.axisColor = "#aaa";

this.font = "8pt Calibri";

this.tickSize = 20;

// relationships

this.context = this.canvas.getContext("2d");

this.rangeX = this.maxX - this.minX;

this.rangeY = this.maxY - this.minY;

this.unitX = this.canvas.width / this.rangeX;

this.unitY = this.canvas.height / this.rangeY;

this.centerY = Math.round(Math.abs(this.minY / this.rangeY) * this.canvas.height);

this.centerX = Math.round(Math.abs(this.minX / this.rangeX) * this.canvas.width);

this.iteration = (this.maxX - this.minX) / 1000;

this.scaleX = this.canvas.width / this.rangeX;

this.scaleY = this.canvas.height / this.rangeY;

// draw x and y axis

this.drawXAxis();

this.drawYAxis();

}

Graph.prototype.drawXAxis = function () {

var context = this.context;

context.save();

context.beginPath();

context.moveTo(0, this.centerY);

context.lineTo(this.canvas.width, this.centerY);

context.strokeStyle = this.axisColor;

context.lineWidth = 2;

context.stroke();

// draw tick marks

var xPosIncrement = this.unitsPerTick * this.unitX;

var xPos, unit;

context.font = this.font;

context.textAlign = "center";

context.textBaseline = "top";

// draw left tick marks

xPos = this.centerX - xPosIncrement;

unit = -1 * this.unitsPerTick;

while (xPos > 0) {

context.moveTo(xPos, this.centerY - this.tickSize / 2);

context.lineTo(xPos, this.centerY + this.tickSize / 2);

context.stroke();

context.fillText(unit, xPos, this.centerY + this.tickSize / 2 + 3);

unit -= this.unitsPerTick;

xPos = Math.round(xPos - xPosIncrement);

}

// draw right tick marks

xPos = this.centerX + xPosIncrement;

unit = this.unitsPerTick;

while (xPos < this.canvas.width) {

context.moveTo(xPos, this.centerY - this.tickSize / 2);

context.lineTo(xPos, this.centerY + this.tickSize / 2);

context.stroke();

context.fillText(unit, xPos, this.centerY + this.tickSize / 2 + 3);

unit += this.unitsPerTick;

xPos = Math.round(xPos + xPosIncrement);

}

context.restore();

};

Graph.prototype.drawYAxis = function () {

var context = this.context;

context.save();

context.beginPath();

context.moveTo(this.centerX, 0);

context.lineTo(this.centerX, this.canvas.height);

context.strokeStyle = this.axisColor;

context.lineWidth = 2;

context.stroke();

// draw tick marks

var yPosIncrement = this.unitsPerTick * this.unitY;

var yPos, unit;

context.font = this.font;

context.textAlign = "right";

context.textBaseline = "middle";

// draw top tick marks

yPos = this.centerY - yPosIncrement;

unit = this.unitsPerTick;

while (yPos > 0) {

context.moveTo(this.centerX - this.tickSize / 2, yPos);

context.lineTo(this.centerX + this.tickSize / 2, yPos);

context.stroke();

context.fillText(unit, this.centerX - this.tickSize / 2 - 3, yPos);

unit += this.unitsPerTick;

yPos = Math.round(yPos - yPosIncrement);

}

// draw bottom tick marks

yPos = this.centerY + yPosIncrement;

unit = -1 * this.unitsPerTick;

while (yPos < this.canvas.height) {

context.moveTo(this.centerX - this.tickSize / 2, yPos);

context.lineTo(this.centerX + this.tickSize / 2, yPos);

context.stroke();

context.fillText(unit, this.centerX - this.tickSize / 2 - 3, yPos);

unit -= this.unitsPerTick;

yPos = Math.round(yPos + yPosIncrement);

}

context.restore();

};

Graph.prototype.drawEquation = function (equation, color, thickness) {

var context = this.context;

context.save();

this.transformContext();

context.beginPath();

context.moveTo(this.minX, equation(this.minX));

for (var x = this.minX + this.iteration; x <= this.maxX; x += this.iteration) {

context.lineTo(x, equation(x));

}

context.restore();

context.lineJoin = "round";

context.lineWidth = thickness;

context.strokeStyle = color;

context.stroke();

context.restore();

};

Graph.prototype.transformContext = function () {

var context = this.context;

// move context to center of canvas

this.context.translate(this.centerX, this.centerY);

context.scale(this.scaleX, -this.scaleY);

};

window.onload = function () {

var myGraph = new Graph({

canvasId: "myCanvas",

minX: -10,

minY: -10,

maxX: 10,

maxY: 10,

unitsPerTick: 1

});

myGraph.drawEquation(function (x) {

return 5 * Math.sin(x);

}, "green", 3);

myGraph.drawEquation(function (x) {

return x * x;

}, "blue", 3);

myGraph.drawEquation(function (x) {

return 1 * x;

}, "red", 3);

};

</script>

</head>

<body>

</body>

</html>

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